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Physics Chapter 8 : Topic 10
Pressure–Volume Relationship
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The pressure-volume relationship of a gas at constant temperature is described by:
Reasoning: Boyle’s law describes the inverse relationship between pressure and volume of a fixed mass of gas at constant temperature.
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According to Boyle’s law, for a fixed mass of gas at constant temperature:
Reasoning: At constant temperature, pressure increases when volume decreases, so pressure is inversely proportional to volume.
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The mathematical equation representing Boyle’s law is:
Reasoning: Boyle’s law states that the product of pressure and volume remains constant at constant temperature.
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A gas occupies $\mathbf{4\ m}^{\mathbf{3}}$ at a pressure of $\mathbf{2\ Pa}$. If its volume is reduced to $\mathbf{2\ m}^{\mathbf{3}}$ atconstant temperature, the new pressure will be:
Reasoning: Using, $\mathbf{P}_{\mathbf{1\ }}\mathbf{V}_{\mathbf{1}}\mathbf{=}\mathbf{P}_{\mathbf{2\ }}\mathbf{V}_{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{2 \times 4 =}\mathbf{P}_{\mathbf{2}}\mathbf{\times 2}$ $\mathbf{\Longrightarrow}$ $\mathbf{P}_{\mathbf{2}}\mathbf{= 4\ Pa}$
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If the volume of a gas is doubled while temperature remains constant, its pressure becomes:
Reasoning: Pressure is inversely proportional to volume, so doubling volume reduces pressure to half.
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A gas is compressed to one-third of its original volume at constant temperature. The pressure becomes:
Reasoning: Since $\mathbf{P \propto}$ $\frac{\mathbf{1}}{\mathbf{V}}\mathbf{\ }$, reducing volume to one-third increases pressure three times.
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In a pressure-volume $\mathbf{(P - V)}$ graph for Boyle’s law, pressure is plotted on the:
Reasoning: Conventionally, pressure is represented on the $\mathbf{y}$-axis and volume on the $\mathbf{x}$-axis.
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The graph of pressure versus volume at constant temperature is:
Reasoning: Because $P\mathbf{=}$ $\frac{\mathbf{k}}{\mathbf{V}}\mathbf{\ }$, the relationship produces a hyperbolic curve.
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A point on a $\mathbf{P - V}$ graph represents:
Reasoning: Each point represents a specific combination of pressure and volume at a given temperature.
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For two different temperatures, the $\mathbf{P - V}$ curves of a gas are different because:
Reasoning: For higher temperatures, molecules have greater kinetic energy, giving a larger value of $\mathbf{PV}$.
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Which graph represents the relationship $\mathbf{P \propto}$ $\frac{\mathbf{1}}{\mathbf{V}}\mathbf{\ }$?
Reasoning: Inverse relationships produce a hyperbola that approaches but never touches the axes.
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At constant temperature, decreasing volume increases pressure because:
Reasoning: Less space causes more frequent collisions with the container walls, increasing pressure.
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Which condition is necessary for Boyle’s law to be valid?
Reasoning: Boyle’s law applies only when temperature and amount of gas remain constant.
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A gas has pressure $\mathbf{100\ kPa}$ and volume $\mathbf{5\ L}$. If pressure becomes $\mathbf{200\ kPa}$ at constant temperature, the volume will be:
Reasoning: $\mathbf{P}_{\mathbf{1\ }}\mathbf{V}_{\mathbf{1}}\mathbf{=}\mathbf{P}_{\mathbf{2\ }}\mathbf{V}_{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{100(5) = 200(}\mathbf{V}_{\mathbf{2}}\mathbf{)}$ $\mathbf{\Longrightarrow}$ $\mathbf{V}_{\mathbf{2}}\mathbf{= 2.5\ L}$
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The area under a $\mathbf{P - V}$ curve represents:
Reasoning: The area under a $\mathbf{P - V}$ curve represents work done during expansion or compression.
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Two gases have the same temperature. For the same volume, the gas with higher pressure has:
Reasoning: Higher pressure results from greater collision frequency or force on container walls.
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A gas is slowly compressed while keeping temperature constant. During this process:
Reasoning: Compression reduces volume, causing pressure to rise according to Boyle’s law.
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A Boyle’s law graph is not a straight line because:
Reasoning: Inverse proportionality produces a curved graph rather than a straight line.
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The equation $\mathbf{P}_{\mathbf{1\ }}\mathbf{V}_{\mathbf{1}}\mathbf{=}\mathbf{P}_{\mathbf{2\ }}\mathbf{V}_{\mathbf{2}}$ can be used when:
Reasoning: The equation is derived from Boyle’s law, which requires constant temperature.
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A gas expands from volume $\mathbf{(V)}$ to $\mathbf{(2V)}$ at constant temperature. The pressure changes from $\mathbf{(P)}$ to:
Reasoning: Doubling volume causes pressure to become half.
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Which statement correctly describes Boyle’s law using particles?
Reasoning: Compression gives particles less space, increasing collisions and pressure.
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On a $\mathbf{P - V}$ graph, moving from a point with large volume to small volume represents:
Reasoning: A decrease in volume represents compression of the gas.
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A gas follows Boyle’s law. Which quantity remains constant?
Reasoning: Boyle’s law states that $\mathbf{(PV)}$ remains constant at constant temperature.
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If the product $\mathbf{(PV)}$ increases for a gas, the most likely reason is:
Reasoning: For a fixed amount of gas, $\mathbf{(PV)}$ is proportional to absolute temperature.
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Which statement about a Boyle’s law curve is correct?
Reasoning: A hyperbola approaches the axes asymptotically but never reaches them.
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If pressure is plotted against $\mathbf{(1\ /\ V)}$, the graph becomes:
Reasoning: Since $\mathbf{P = k\ (1\ \ /V)}$, pressure is directly proportional to inverse volume.
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Why is temperature kept constant in Boyle’s law experiments?
Reasoning: Constant temperature ensures average kinetic energy of molecules remains unchanged.
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A gas sample is compressed to a smaller volume without changing temperature. Which quantity increases?
Reasoning: Reduced volume increases collisions with container walls, increasing pressure.
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The constant in Boyle’s law equation $\mathbf{(PV = k)}$ depends on:
Reasoning: The value of $\mathbf{(k)}$ depends on temperature and quantity of gas.
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A horizontal line on a $\mathbf{P - V}$ graph would indicate:
Reasoning: A horizontal line means pressure remains unchanged while volume varies.
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